The Truth Value Algebra of Type-2 Fuzzy Sets: Order Convolutions of Functions on the Unit Interval, 1st Edition (e-Book) book cover

The Truth Value Algebra of Type-2 Fuzzy Sets

Order Convolutions of Functions on the Unit Interval, 1st Edition

By John Harding

Chapman and Hall/CRC

254 pages

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Hardback: 9781498735278
pub: 2016-03-09
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pub: 2016-03-30
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Description

Type-2 fuzzy sets extend both ordinary and interval-valued fuzzy sets to allow distributions, rather than single values, as degrees of membership. Computations with these truth values are governed by the truth value algebra of type-2 fuzzy sets. The Truth Value Algebra of Type-2 Fuzzy Sets: Order Convolutions of Functions on the Unit Interval explo

Table of Contents

The Algebra of Truth Values. Properties of the Type-2 Truth Value Algebra. Subalgebras of the Type-2 Truth Value Algebra. Automorphisms. T-Norms and T-Conorms. Convex Normal Functions. Varieties Related to M. Type-2 Fuzzy Sets and Bichains. Categories of Fuzzy Relations. The Finite Case. Appendix. Bibliography. Index.

About the Author

John Harding is a professor in the Department of Mathematical Sciences at New Mexico State University. He is the author/coauthor of roughly 70 papers, president of the International Quantum Structures Association, and member of the editorial board of Order and the advisory board of Mathematica Slovaca. His research focuses on order theory and its applications, particularly applications to topology and logic, the foundations of quantum mechanics, completions, and fuzzy sets. He earned his Ph.D. in mathematics from McMaster University.

Carol Walker was a professor in the Department of Mathematical Sciences at New Mexico State University before retiring in 1996. She was department head for 14 years and associate dean of arts and sciences and director of the Arts and Sciences Research Center for three years. She is the author/coauthor of more than 35 papers as well as several textbooks and technical manuals. Her research focuses on algebra, including abelian group theory, applications of category theory to abelian groups and modules, and algebraic aspects of the mathematics of fuzzy sets. She earned her Ph.D. in mathematics from New Mexico State University.

Elbert Walker was a professor in the Department of Mathematical Sciences at New Mexico State University before retiring in 1987. He then worked at the U.S. National Science Foundation for two years. He is the author/coauthor of about 95 research papers and several books. His research interests include abelian group theory, statistics, and the mathematics of fuzzy sets and fuzzy logic. He earned his Ph.D. in mathematics from the University of Kansas.

Subject Categories

BISAC Subject Codes/Headings:
MAT002000
MATHEMATICS / Algebra / General
MAT003000
MATHEMATICS / Applied
MAT028000
MATHEMATICS / Set Theory